GATE 2015 EE (EE2) – Question 65
Control Systems · Mathematical modelling and representation of systems, Feedback principle, Transfer function, Block diagrams and Signal flow graphs · 2 marks · Multiple choice
The system obeys $\dot x_1=2x_1+x_2+u$, $\dot x_2=-2x_1+u$, y=3x1. Its zero-state transfer Y(s)/U(s) is
- $3(s+1)/(s^2-2s+2)$
- $3(2s+1)/(s^2-2s+1)$
- $(s+1)/(s^2-2s+1)$
- $3(2s+1)/(s^2-2s+2)$
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Show answer and explanation
Correct answer: (A) $3(s+1)/(s^2-2s+2)$
Explanation
Under zero initial conditions, sX2=−2X1+U, so X2=(−2X1+U)/s. Substitute this into sX1=2X1+X2+U.
Multiplying by s and collecting gives (s²−2s+2)X1=(s+1)U. Since Y=3X1, the transfer is **3(s+1)/(s²−2s+2), A**.
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